Optical coherence tomography may be used in a variety of medical applications. One method, swept source optical coherence tomography (SS-OCT) or optical frequency domain imaging (OFDI), as it is sometimes called, is used often for its simplicity, flexibility, and signal to noise ratio.
An example SS-OCT (or OFDI) system 100 is illustrated in FIG. 1. The swept source 110 is a narrow bandwidth laser whose frequency is swept in time. The output of the swept source 110 is directed to a beam splitter 120 that directs some of the light to a reference path 124 and some of the light to the sample path 122. The reference path 124 may include some optional elements 130 such as dispersion compensation elements and/or path length changing elements in some designs. The light in the sample path 122 is directed to the sample 10 under investigation by light delivery and collection optics 140, and the light backscattered from the sample 10 under investigation is collected by the light delivery and collection optics 140. The light backscattered by the sample 10 is then combined with the light from the reference path 124 in the beam combiner 150 and directed to a photo detector 160 where the interference signal between the two optical fields is detected. The interference signal from the photo detector 160 is directed to the analog to digital (A/D) converter 170. Finally, the output of the A/D converter 170 is sent to the data analysis system (DAS) 180.
The electrical fields from the reference beam 124, Er(t) and the electrical field backscattered from the sample 10, Es(t) areEr(t)=Er0e−i2πν(t)t  1)andEs(t)=ΣnEsne−i2πν(t+τn)(t+τn),  2)where Er0 represents the reference beam 124 electric field amplitude at the photo detector 160, and Esn represents the electric field amplitude of the backscattering from nth sample 10 element. ν(t) represents the laser frequency at the photo detector 160 at time t, and the ν(t-τn) represents the nth sample 10 element backscattered laser frequency at the photo detector 160 at time t+τn. τn represents the time delay between the reference beam 124 and the time when the backscattering from element n of the sample 10 arrives at the photo detector 160. The summation in Eq. 2 is over all of the n sample 10 spatial elements.
The interference signal between the reference light 124 and the light backscattered by a sample 10 on the photo detector 160 produces a signal proportional to the product of the reference field amplitude times, the backscattered field amplitude from the spatial elements in the sample 10 at the sum, and difference frequencies between the reference field frequency and backscattered sample 10 element frequency,VPD(t)∝Σn[|Er0||Esn|e−i2π[ν(t)−(ν(t+τn)]t+Er0||Esn|e−i2π[ν(t)+(ν(t+τn)]t]  3)orVPD(t)=Σn[VPD_n_amp(e−i2π[ν(t)−(ν(t+τn)]t+e−i2π[ν(t)+(ν(t+τn)]t)],  4)where VPD_n_amp represents the signal amplitude generated by the photo detector 160 due to the interference between the nth sample 10 element backscattering and the reference beam 124. The first term in the summation on the right hand side of Eq. 4 represents the unique beat note signal generated by the frequency difference for the nth spatial element. The second term in Eq. 4 represents the sum of two optical frequencies. Optical frequencies are many orders of magnitude too fast for electrical photo detectors 160 to detect. Therefore, the sum frequency term is integrated to zero by the photo detector 160, and hence the detected interference signal due to the all of the sample element 10 backscattering is given by,VPD(t)=Σn[VPD_n_ampe−i2π[ν(t)−(ν(t+τn)]t].  5)
The photo detector 160 signal due to the nth sample 10 element is,VPD_n(t)=VPD_n_ampe−i2π[ν(t)−(ν(t+τn)]t.  6)
From Eq. 6 it is clear that the nth sample 10 element produces a sinusoidal oscillation at a frequency,νfringe_n=ν(t)−ν(t+τn),  7)where, νfringe_n is uniquely determined by the time delay between the reference path 124 and the nth sample 10 element path, τn. If the sample 10 is stationary during the measurement, then the spatial elements can be uniquely located in space by the fringe frequencies. For the human eye to be considered stationary, these measurements need to be completed in under 0.2 seconds. For full 3-D medical scan of the human eye, approximately two thousand or more A-scans must be performed within 0.2 seconds. These requirements result in fringe frequencies that can easily exceed 1 GHz. For example, assuming 2000 A-scans are needed to measure the human eye, then every A-scan must be completed in less than 5 microseconds. The depth of a common human eye, deye can be as high as 35 mm, which corresponds to a maximum time delay of,
                                          τ                          ma              ⁢                                                          ⁢              x                                =                                                    2                ⁢                                  d                  eye                                ⁢                                  n                  eye                                            c                        =                          0.31              ⁢                                                          ⁢              ns                                      ,                            8        )            where, neye represents the index of refraction of the eye at 1050-nm, and c represents the speed of light in vacuum. Typical swept frequency lasers are tuned around a center wavelength of λ over spectral range, Δλ. Assuming a laser center wavelength of 1050-nm, a spectral sweep range of 100-nm and a linear frequency swept, then the maximum fringe frequency is,
                                          ν                          fringe              ⁢                                                          ⁢              _              ⁢                                                          ⁢              n              ⁢                                                          ⁢              _              ⁢                                                          ⁢              ma              ⁢                                                          ⁢              x                                =                                                    dv                dt                            ⁢                              τ                                  ma                  ⁢                                                                          ⁢                  x                                                      =                                                            c                  ⁢                                                                          ⁢                  Δλ                                                  λ                  2                                            ⁢                              1                                  T                  Ascan                                            ⁢                              τ                                  ma                  ⁢                                                                          ⁢                  x                                                                    ,                            9        )            where νfringe_n_max represents the highest fringe frequency generated in a full measurement of a human eye, and TAscan represents the time for one A-scan. Note that higher fringe frequencies are present if the laser scan is nonlinear. For the characteristic human eye and swept source OCT specifications listed above,νfringe_n_max=1.7 GHz.  10)
The minimum sampling rate required to accurately reconstruct a noiseless uniformly sampled sinusoid is theoretically a minimum of twice νfringe_n_max according to the Nyquist criterion. If there are interfering signals, noise, and/or non-uniform sampling, then the sample rate must be significantly higher than twice νfringe_n_max. In the case of SS-OCT, there is usually non-uniform sampling due to imperfection in the k-clock and considerable interference from the other fringe frequencies, νfringe_n, for example. Even if the laser's instantaneous coherence length limits the maximum measureable time delay to approximately ¼ the length of the human eye, the sampling rate of the analog to digital converter still needs to be significantly higher than the Nyquist rate of 0.8 Gsps. In addition, because of the multitude of signals simultaneously generated by the SS-OCT system, the analog to digital converters must have 12-bit resolution. High-resolution analog to digital converters with 1 giga samples per second (Gsps) rate are often more than a factor of ten more costly than ½ Gsps high resolution analog to digital converters.
In electronics, a mixer or frequency mixer is a nonlinear electrical circuit that creates new frequencies from two signals applied to it. In the most common application, two signals at frequencies ν1 and ν2 are applied to a mixer, and the mixer produces new signals at the sum ν1+ν2 and difference ν1−ν2 of the original frequencies. Mixers are widely used to shift signals from one frequency range to another, a process known as heterodyning. When the useful signal is contained in the difference frequency mixed signal, it is said to be down shifted or down converted. Such mixers often comprise nonlinear components such as diodes.
A well-known application of down conversion is the reception of FM radio broadcast signals; these are broadcast at around 100 MHz but contain audio information below 20 KHz. A local oscillator in the radio receiver produces a signal at the broadcast frequency (the tuner) which is mixed with the received signal; the difference frequency is then low pass filtered to produce the audio content.